Question

What 3-digit number is a perfect square and a perfect cube?

Answer 1

`729=9^3=27^2`

Explanation:

The answer must be `a^6` for some integer `a` due to the properties of exponentiation. Only `3^6 = 729` lies in the required range.

`3^6 = (3^2)^3 = 9^3`

`3^6 = (3^3)^2 = 27^2`